Reaction-diffusion systems: stabilizing effect of conditions described by quasivariational inequalities

Milan Kučera

Czechoslovak Mathematical Journal (1997)

  • Volume: 47, Issue: 3, page 469-486
  • ISSN: 0011-4642

Abstract

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Reaction-diffusion systems are studied under the assumptions guaranteeing diffusion driven instability and arising of spatial patterns. A stabilizing influence of unilateral conditions given by quasivariational inequalities to this effect is described.

How to cite

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Kučera, Milan. "Reaction-diffusion systems: stabilizing effect of conditions described by quasivariational inequalities." Czechoslovak Mathematical Journal 47.3 (1997): 469-486. <http://eudml.org/doc/30377>.

@article{Kučera1997,
abstract = {Reaction-diffusion systems are studied under the assumptions guaranteeing diffusion driven instability and arising of spatial patterns. A stabilizing influence of unilateral conditions given by quasivariational inequalities to this effect is described.},
author = {Kučera, Milan},
journal = {Czechoslovak Mathematical Journal},
keywords = {reaction-diffusion systems; unilateral conditions; bifurcation; quasivariational inequalities; spatial patterns; diffusion-driven instability; unilateral conditions; stationary spatially nonhomogeneous solutions; domain of stability},
language = {eng},
number = {3},
pages = {469-486},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Reaction-diffusion systems: stabilizing effect of conditions described by quasivariational inequalities},
url = {http://eudml.org/doc/30377},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Kučera, Milan
TI - Reaction-diffusion systems: stabilizing effect of conditions described by quasivariational inequalities
JO - Czechoslovak Mathematical Journal
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 3
SP - 469
EP - 486
AB - Reaction-diffusion systems are studied under the assumptions guaranteeing diffusion driven instability and arising of spatial patterns. A stabilizing influence of unilateral conditions given by quasivariational inequalities to this effect is described.
LA - eng
KW - reaction-diffusion systems; unilateral conditions; bifurcation; quasivariational inequalities; spatial patterns; diffusion-driven instability; unilateral conditions; stationary spatially nonhomogeneous solutions; domain of stability
UR - http://eudml.org/doc/30377
ER -

References

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  1. Bifurcation points of reaction-diffusion systems with unilateral conditions, Czechoslovak Math. J. 35 (1985), 639–660. (1985) MR0809047
  2. Eigenvalues of inequalities of reaction-difusion type and destabilizing effect of unilateral conditions, Czechoslovak Math. J. 36 (1986), 116–130. (1986) MR0822872
  3. Reaction-diffusion systems: Destabilizing effect of unilateral conditions, Nonlinear Analysis, Theory, Methods, Applications 12 (1988), 1173–1192. (1988) MR0969497
  4. Nonlinear Differential Equations, Elsevier, Amsterdam, 1980. (1980) MR0558764
  5. Stability and bifurcation problems for reaction-diffusion system with unilateral conditions, Equadiff 6, Vosmanský, J. – Zlámal, M. (eds.), Brno, Universita J. E. Purkyně, 1986, pp. 227–234. (1986) MR0877129
  6. Bifurcation for quasi-variational inequalities of reaction-diffusion type, Stability and Applied Analysis of Continuous Media, Pitagora, Bologna, Vol. 3, No. 2, 1993, pp. 111–127. (1993) 
  7. Bifurcation of solutions to reaction-diffusion system with unilateral conditions, Navier-Stokes Equations and Related Nonlinear Problems, A. Sequeira (ed.), Plenum Press, New York, 1995, pp. 307–322. (1995) MR1373224
  8. 10.1016/0362-546X(95)00055-Z, Nonlin. Anal., T. M. A. 27 (1996), no. 3, 249–260. (1996) MR1391435DOI10.1016/0362-546X(95)00055-Z
  9. Problèmes aux limits non homogènes, Dunod, Paris, 1968. (1968) 
  10. 10.1111/j.1749-6632.1979.tb29492.x, Ann. N.Y. Acad. Sci. 316 (1979), 490–521. (1979) MR0556853DOI10.1111/j.1749-6632.1979.tb29492.x
  11. Implicit variational problems and quasi variational inequalities, Nonlinear Operators and the calculus of Variations (Summer School, Univ. Libre Bruxelles, Brussels), Lecture Notes in Math., Vol. 543, Springer Berlin, pp. 83–156. Zbl0346.49003MR0513202
  12. 10.1137/0513037, SIAM J. Math. Analysis 13 (1982), 555–593. (1982) Zbl0505.76103MR0661590DOI10.1137/0513037
  13. Bifurcation points and eigenvalues of inequalities of reaction-diffusion type, J. reine angew. Math. 380 (1987), 1–13. (1987) Zbl0617.35053MR0916198
  14. Topics in Stability and Bifurcation Theory, Lecture Notes in Mathematics 309, Springer-Verlag, Berlin-Heidelberg-New York, 1973. (1973) Zbl0248.35003MR0463624
  15. Projections on convex sets in Hilbert space and spectral theory, Contributions to Nonlinear Functional Analysis, E. H. Zarantonello (ed.), Academic Press, New York, 1971. (1971) Zbl0281.47043

Citations in EuDML Documents

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  1. Jamol I. Baltaev, Milan Kučera, Martin Väth, A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions
  2. Jan Eisner, Milan Kučera, Spatial patterns for reaction-diffusion systems with conditions described by inclusions
  3. Jan Eisner, Milan Kučera, Martin Väth, A variational approach to bifurcation points of a reaction-diffusion system with obstacles and Neumann boundary conditions
  4. Lucie Kárná, Milan Kučera, Bifurcations for a problem with jumping nonlinearities
  5. Jan Eisner, Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions

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